逻辑回归机器学习

线性组合的基础上加上非线性变换

y=kx+b

torch.nn.linear(input,output)

torch.sigmoid(input)

torch.nn.BCELoss()

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import numpy as np
import torch
import matplotlib.pyplot as plt
from onnxslim.core import optimize

x = np.linspace(-5,5,20, dtype=np.float32)//-5,5之间随机生成20个数
_b=1/(1 + np.exp(-x))//通过变换得到_b
y = np.random.normal(_b,0.005)//在此基础上加上0.05的噪声来获得y

x = np.float32(x.reshape(-1,1))
y = np.float32(y.reshape(-1,1))

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class LogicRegressionModel(torch.nn.Module):
    def __init__(self, input_dim, output_dim):
        super(LogicRegressionModel, self).__init__()
        self.linear = torch.nn.Linear(input_dim, output_dim)

    def forward(self, x):
        out = torch.sigmoid(self.linear(x))//sigmoid 函数的作用是将输入的实数映射到区间 (0, 1) 上。在神经网络中，激活函数可以引入非线性因素，使得网络能够学习和表示复杂的模式。对于逻辑回归模型来说，sigmoid 函数将线性层的输出转换为一个概率值，即表示输入属于某一类别的可能性。在这段代码中，torch.sigmoid(self.linear(x)) 就是将线性层的输出通过 sigmoid 函数进行变换，得到最终的输出 out，这个 out 的值在 0 到 1 之间，可以被解释为一个概率预测值。
        return out

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input_dim = 1
output_dim = 1
model = LogicRegressionModel(input_dim, output_dim)
criterion = torch.nn.BCELoss()在二分类问题中，我们希望模型输出一个概率值，表示输入样本属于正类的可能性。二元交叉熵损失就是用来衡量模型预测的概率值与真实标签（通常为 0 或 1，表示负类和正类）之间的差距。如果模型预测的概率值与真实标签越接近，那么二元交叉熵损失就越小；反之，损失就越大。
learning_rate = 0.01
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)

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import numpy as np
import torch
import matplotlib.pyplot as plt
from onnxslim.core import optimize

x = np.linspace(-5,5,20, dtype=np.float32)
_b=1/(1 + np.exp(-x))
y = np.random.normal(_b,0.005)

x = np.float32(x.reshape(-1,1))
y = np.float32(y.reshape(-1,1))


class LogicRegressionModel(torch.nn.Module):
    def __init__(self, input_dim, output_dim):
        super(LogicRegressionModel, self).__init__()
        self.linear = torch.nn.Linear(input_dim, output_dim)

    def forward(self, x):
        out = torch.sigmoid(self.linear(x))
        return out


input_dim = 1
output_dim = 1
model = LogicRegressionModel(input_dim, output_dim)
criterion = torch.nn.BCELoss()
learning_rate = 0.01
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)

for epoch in range(100):
    epoch +=1
    inputs = torch.from_numpy(x).requires_grad_()
    labels = torch.from_numpy(y)

    optimizer.zero_grad()
    outputs = model(inputs)
    loss = criterion(outputs, labels)
    loss.backward()
    optimizer.step()
    print('epoch {}, loss {}'.format(epoch + 1, loss.item()))

# 绘制结果
predicted_y=model(torch.from_numpy(x).requires_grad_()).data.numpy()
print("标签y",y)
print("预测y",predicted_y)
plt.clf()
predicted=model(torch.from_numpy(x).requires_grad_()).data.numpy()
plt.plot(x,y,'go',label='True data',alpha=0.5)
plt.plot(x,predicted_y,'--',label='Predictions',alpha=0.5)
plt.legend(loc='best')
plt.show()